For the problems below, state the null and alternate hypothesis, draw a picture
ID: 3150837 • Letter: F
Question
For the problems below, state the null and alternate hypothesis, draw a picture showing the nature of the test, decide what conclusion can be made from the given P-value and write a statement interpreting your decision in the context of the original claim.
The industrial world shares this common goal: Improve quality by reducing variation. Quality control engineers want to ensure that a product has an acceptable mean, but they also want to produce items of consistent quality so that there will be few defects. The Newport Bottling Company had been manufacturing cans of cola with amounts having a standard deviation of 0.051 oz. A new bottling machine is tested, and a simple random sample of 24 cans results in s = 0.039 oz. Use a 0.05 significance level to test the claim that cans of cola from the new machine have amounts with a standard deviation that is less than 0.051 oz.
The test statistic is constructed and a P-value of 0.0584 is found.
Explanation / Answer
Ho: o^2=0.002601
Ha: o^2 < 0.002601
The test statistic is
Chisquare =(n-1)*s^2/o^2
=(24-1)*(0.039^2) /(0.051 )^2
= 13.4498
Given a=0.05, the critical value of chisquare with df=n-1=23 is 35.17246 (from chisquare table)
Since 13.4498 is less than 35.17246, we do not reject Ho.
So we can conclude that the variance in the number of patients seen per day equal to 0.002601 (i.e equal to 0.051 standard deviation)